Find the equation of the curve which is such that the area of the rectangle constructed on the abscissa of and the initial ordinate of the tangent at this point is a constanta `=a^2`.

Find the equation of the curve which is such that the area of the rectangle constructed on the abscissa of any point and the intercept of the tangent at this point on the y-axis is equal to 4.

Find the equation of the curve in which the perpendicular from the origin on any tangent is equal to the abscissa of the point of contact.

The curve in which the slope of the tangent at any point equal the ratio of the abscissa to the ordinate of the point is

Find the equation of a curve such that the projection of its ordinate upon the normal is equal to its abscissa.

Find the equation of a curve such that the projection of its ordinate upon the normal is equal to its abscissa.

The equation of the curve which is such that the portion of the axis of x cut-off between the origin and tangent at any point is proportional to the ordinate of that point is

The equation of the curve which is such that the portion of the axis of x cut off between the origin and tangent at any point is proportional to the ordinate of that point is

Find the equation of the curve such that the square of the intercept cut off by any tangent from the y-axis is equal to the product of the co-ordinate of the point of tangency.

Find the curve such that the area of the trapezium formed by the co-ordinate axes, ordinate of an arbitrary point & the tangent at this point equals half the square of its abscissa.

The equation of the curve,passing through (2, 5) and having the area of triangle formed by the X-axis,the ordinate of a point on the curve and the tangent at the point 5 sq.units as